Multiple-input Multiple-output Frequency-selective Fading Channel Research Articles

Doppler Spread Estimation in MIMO Frequency-Selective Fading Channels

One of the main challenges in high-speed mobile communications is the presence of large Doppler spreads. Thus, accurate estimation of maximum Doppler spread (MDS) plays an important role in improving the performance of the communication link. In this paper, we derive the data-aided (DA) and non-data-aided (NDA) Cramer–Rao lower bounds (CRLBs) and maximum likelihood estimators (MLEs) for the MDS in multiple-input multiple-output (MIMO) frequency-selective fading channel. Moreover, a low-complexity NDA-moment-based estimator (MBE) is proposed. The proposed NDA-MBE relies on the second- and fourth-order moments of the received signal, which are employed to estimate the normalized squared autocorrelation function of the fading channel. Then, the problem of MDS estimation is formulated as a non-linear regression problem, and the least-squares curve-fitting optimization technique is applied to determine the estimate of the MDS. This is the first time in the literature, when DA- and NDA-MDS estimation is investigated for MIMO frequency-selective fading channel. Simulation results show that there is no significant performance gap between the derived NDA-MLE and NDA-CRLB, even when the observation window is relatively small. Furthermore, the significant reduced-complexity in the NDA-MBE leads to low root-mean-square error over a wide range of MDSs, when the observation window is selected large enough.

Energy-Efficient Spatial Modulation Over MIMO Frequency-Selective Fading Channels

In this paper, an energy-efficient spatial modulation (SM), which is called joint space and time dispersion modulation (STdM), is proposed for the multiple-input multiple-output (MIMO) frequency-selective fading channel. The proposed scheme extends the recent concept of SM to both space and time dispersion dimensions. Specifically, in the STdM scheme, only 1 out of N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> transmit antennas (TAs) is active in 1 out of L-1 channel time slots, where N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> and L are the number of TAs and the channel time dispersion length, respectively. Moreover, the information is carried by three units: active-channel time-slot index, active-antenna index, and modulation symbol. Compared with SM, the proposed STdM employs a new dimension, i.e., the passive-channel time slot, to convey information. Therefore, the proposed STdM is expected to have energy efficiency superiority over SM, similar to the superiority of SM over the conventional MIMO scheme, which is then validated by simulations.

Orthogonal Affine Precoding and Decoding for Channel Estimation and Source Detection in MIMO Frequency-Selective Fading Channels

A new affine precoding and decoding method for multiple-input multiple-output (MIMO) frequency-selective fading channels is proposed. The optimal design of the affine precoder consists of a linear precoder and a training sequence, which is superimposed on the linearly precoded data in an orthogonal manner. The channel is estimated independently of the data, while the training sequence is completely nulled out in the source data detection. Furthermore, the optimal power allocation between the data and training signals is also analytically derived. Simulation results show that the proposed method is significantly better than other affine precoding methods with regard to source detection performance and computational complexity.

Reduced-complexity equalization techniques for ISI and MIMO wireless channels in iterative decoding

Two reduced-complexity soft-input soft-output trellis decoding techniques are presented in this paper for equalizing single-input single-output intersymbol interference (ISI) channels and multiple-input multiple-output (MIMO) frequency selective fading channels. Given a trellis representing an ISI channel, the soft-output M-algorithm (SOMA) reduces the complexity of equalization by retaining only the best M survivors at each trellis interval. The remaining survivors are discarded. The novelty of the SOMA is the use of discarded paths to obtain soft-information. Through a simple update-and-discard procedure, the SOMA extracts reliable soft-information from discarded paths which enables a large trellis to be successfully decoded with a relatively small value of M. To decode a trellis representing a MIMO frequency selective fading channel, two challenges are faced. Not only that the trellis has a large number of states, the number of branches per trellis interval is also enormous. The soft-output trellis/tree M-algorithm (SOTTMA) expands each trellis interval into a tree-like structure and performs the M-algorithm twice: once at each trellis interval to reduce the number of states and the other at each tree sub-level to remove unwanted branches. With the proposed technique, high-order trellises with million of branches per interval can be decoded with modest complexity.

Soft input soft output Kalman equalizer for MIMO frequency selective fading channels

We consider the Kalman filter for equalization of a multiple-input multiple-output (MIMO), frequency selective, quasi-static fading channel. More specifically, we consider a coded system, where the incoming bit stream is convolutionally encoded, interleaved and then spatially multiplexed across the transmit antennas. Each substream is modulated into M-ary symbols before being transmitted over a frequency selective channel. At the receiver, we propose to use the Kalman filter as a low complexity MIMO equalizer, as opposed to the trellis based maximum a-posteriori (MAP) equalizer whose computational complexity grows exponentially with the channel memory, the number of transmit antennas and the spectral efficiency (bits/s/Hz) of the system. We modify the structure of the Kalman filter and enable it to process the a-priori (soft) information provided by the channel decoder, thereby allowing us to perform iterative (turbo) equalization on the received sequence. The iterative equalizer structure is designed for general M-ary constellations. We also propose a low complexity version of the above algorithm whose performance is comparable to its full complexity counterpart, but which achieves a significant complexity reduction. We demonstrate via simulations that for higher order constellations, when sufficient number of receive antennas are available (e.g. for a 2 transmitter, 3 receiver system, QPSK), the performance of the proposed algorithms after 4 iterations is within 1.5 dB of the non-iterative MAP algorithm with close to an order of magnitude complexity reduction. By objectively quantifying the complexity of all the considered algorithms we show that the complexity reduction for the proposed schemes becomes increasingly significant for practical systems with moderate to large constellation sizes and a large number of transmit antennas

On the design of space-time and space-frequency codes for MIMO frequency-selective fading channels

The authors introduced an algebraic design framework for space-time coding in flat-fading channels . We extend this framework to design algebraic codes for multiple-input multiple-output (MIMO) frequency-selective fading channels. The proposed codes strive to optimally exploit both the spatial and frequency diversity available in the channel. We consider two design approaches: The first uses space-time coding and maximum likelihood decoding to exploit the multi-path nature of the channel at the expense of increased receiver complexity. Within this time domain framework, we also propose a serially concatenated coding construction which is shown to offer a performance gain with a reasonable complexity iterative receiver in some scenarios. The second approach utilizes the orthogonal frequency division multiplexing technique to transform the MIMO multipath channel into a MIMO flat block fading channel. The algebraic framework is then used to construct space-frequency codes (SFC) that optimally exploit the diversity available in the resulting flat block fading channel. Finally, the two approaches are compared in terms of decoder complexity, maximum achievable diversity advantage, and simulated frame error rate performance in certain representative scenarios.